Pith Number

pith:GCYR7GCJ

pith:2011:GCYR7GCJLIB2LQKON6OV3P2WYQ

not attested not anchored not stored refs pending

Covolumes of nonuniform lattices in PU(n, 1)

Matthew Stover, Vincent Emery

arxiv:1107.5281 v2 · 2011-07-26 · math.GT · math.GR · math.NT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GCYR7GCJLIB2LQKON6OV3P2WYQ}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T04:02:54.390059Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

30b11f98495a03a5c14e6f9d5dbf56c413b7ea5c1deda0d85713f11cd116739f

Aliases

arxiv: 1107.5281 · arxiv_version: 1107.5281v2 · doi: 10.48550/arxiv.1107.5281 · pith_short_12: GCYR7GCJLIB2 · pith_short_16: GCYR7GCJLIB2LQKO · pith_short_8: GCYR7GCJ

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/GCYR7GCJLIB2LQKON6OV3P2WYQ \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 30b11f98495a03a5c14e6f9d5dbf56c413b7ea5c1deda0d85713f11cd116739f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b579aacac9fa2de6eaaecdbd11b67676390386a65e928e5a45405be6e28025e2",
    "cross_cats_sorted": [
      "math.GR",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-07-26T18:15:22Z",
    "title_canon_sha256": "5cd0fa5baaeaa8e4dcab221038988aed1a1e2680d91909fabe6e0bfe321de19c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.5281",
    "kind": "arxiv",
    "version": 2
  }
}